1. Field of Invention
The present invention relates to a method for evaluating a virtual metrology system is disclosed. More particularly, the present invention relates to a method for evaluating reliance level of the virtual metrology system suitable for use in production equipment of a semiconductor or thin film transistor liquid crystal display (TFT-LCD) plant.
2. Description of Related Art
In most semiconductor and TFT-LCD plants, product quality is monitored by sample-testing, that is the products in manufacturing process are selectively tested periodically, or dummy materials (such as monitoring wafers or glass) are applied in a manufacturing process and tested to determine the acceptability of the process quality. The conventional method generally assumes that abnormal conditions regarding process quality of production equipment do not occur abruptly, and thus measurement results of the selected products or the dummy materials can be used to infer the product quality during a specific production period. However, the conventional monitoring method can merely know the quality of the selected products or dummy materials being tested, and cannot know the quality of the products in-between the selected ones. If the production equipment exhibits abnormalities during any two selected tests, the conventional monitoring method cannot identify the abnormalities sufficiently quickly, thus inferior products may be produced.
For resolving the above problem, comprehensive testing of all products is necessary. However, testing every product requires the installation of large amounts of metrology equipment and also requires considerable cycle time. Large amounts of dummy materials are also wasted. Therefore, a virtual metrology method must be developed for monitoring process quality without taking actual measurements, such that quality of production process can be seamlessly monitored in real time. Moreover, virtual metrology is also essential for wafer-to-wafer advanced process control.
When a virtual metrology system (VMS) is used to conjecture a virtual measurement value of a product, if the product happens to be a selected test sample that has an actual measurement value, then the conjecture error of the virtual measurement value can be evaluated. However, in most cases the product is not a selected test sample, such that no actual measurement value can be provided for comparison with the virtual measurement value. Thus, the accuracy of the virtual measurement value is unknown. Users consequently cannot appreciate in real time what the reliance level of the virtual measurement value is, causing hesitation in application. This phenomenon is attributed to the so-called applicability or manufacturability problem of a VMS.
While surveying the relevant research, Chryssolouris et al. (G. Chryssolouris, M. Lee, and A. Ramsey, “Confidence Interval Prediction for Neural Network Models,” IEEE Transactions on Neural Networks, vol. 7, no. 1, pp. 229-232, 1996.) and Rivals/Personnaz (I. Rivals, and L. Personnaz, “Construction of Confidence Intervals for Neural Networks Based on Least Square Estimation,” Neural Networks, vol. 13, pp. 463-484, 2000.), presented methods of establishing confidence intervals in neural-network prediction models. However, the confidence intervals they established are not sufficiently practical for resolving the manufacturability problem of a VMS.
Djurdjanovic et al. (D. Drurdjanovic, J. Lee, and J. Ni, “Watchdog Agent—An Infotronics-Based Prognostics Approach for Product Performance Degradation Assessment and Prediction,” Advanced Engineering Informatics, vol. 17, pp. 109-125, 2003.) as well as Yan and Lee (J. Yan and J. Lee, “Introduction of Watchdog Prognostics Agent and Its Application to Elevator Hoistway Performance Assessment,” Journal of the Chinese Institute of Industrial Engineers, vol. 22, no. 1, pp. 56-63, 2005.), presented the concept of performance confidence value (CV) for assessing performance degradation using a watchdog prognostics agent. However, the above studies do not set up a proper threshold value for the performance CV. The proposed assessment method can thus only obtain a numerical performance confidence value, but cannot explicitly determine whether the performance CV is reliable or not.